My point about braille was as follows:

If we assume that integration by hand is a needed skill and most functions we come across can't be integrated by hand, the knowledge of integrating by hand has the same type of application that learning to read braille when not blind does. Sure we could use braille to read, but it's better not to and sometimes it won't even work. Likewise, we could integrate by hand, but it's better not to and sometimes it won't work.

One reason I like economics so much is the lessons it teaches that apply to just about everything. Like opportunity cost. Even though learning integration by hand is flexing a brain muscle, brain resources and time resources are finite and I think integrating by hand is an opportunity cost when we could be doing more productive things instead. It's like long division of ten figures. We gain no real direct value from doing it. A calculator is easier, more accurate, faster, and leaves more resources for other things.

It's funny, I only know how to do long division because when I went back to college after forever away from math, I had to relearn it because my intermediate algebra course didn't allow calculators. Yet since calculators have been allowed for me, I haven't used it once and I will never use it and a decade from now I will probably forget how to do it. It's like something I heard the other day: "if you're using a calculator to do 2+2, you're doing math right." This is because the comparative advantage (heart economics) humans have is analytics and we shouldn't waste our time on rote computation.